Varactor Element and Low Distortion Varactor Circuit Arrangement

ABSTRACT

A varactor element having a junction region, in which the depletion capacitance of the varactor element varies when a reverse bias voltage is applied to the varactor element. The varactor element has an exponential depletion capacitance-voltage relation, e.g. obtained by providing a predetermined doping profile in the junction region. The varactor element can be used in a narrow tone spacing varactor stack arrangement, in which two varactor elements are connected in an anti-series configuration. A low impedance path for base band frequency components between a control node and each of two RF connection nodes is provided, while for fundamental and higher order harmonic frequencies, a high impedance path is provided.

FIELD OF THE INVENTION

The present invention relates to a varactor element having a junctionregion, in which the depletion capacitance of the varactor elementvaries when a reverse bias voltage is applied to the varactor element.Such a varactor element is also known as varactor diode, tunable diode,or voltage controlled capacitor.

PRIOR ART

Such varactor elements are known, and the behavior is well understood.In textbooks, it can be found that for diode based varactor elements,the capacitance voltage characteristic is in the form of

${{C(V)} = \frac{K}{\left( {\varphi + V} \right)^{m}}},$

in which C(V) is the capacitance as function of the total (reverse)voltage V across the diode, φ is the built-in potential of the diode, mis the power law exponent of the diode capacitance and K is thecapacitance constant. For a diode with a uniform doping profile, m=0.5,and for a diode with a hyper-abrupt junction, m≈1.5. Such acharacteristic however limits the application of varactors in certainhigh quality applications, such as low distortion varactor stacks,especially when used in devices designed for operation with narrow tonespacing signals, such as in many modern day communications systems (seee.g. K. Buisman, L. C. N. de Vreede, L. E. Larson, M. Spirito, A.Akhnoukh, T. L. M. Scholtes and L. K. Nanver, “‘Distortion free’varactor diode topologies for RF adaptivity,” in 2005 IEEE MTT-S Int.Microwave Symp. Dig., Long Beach, Calif., June. 2005).

In order to overcome these drawbacks, recently varactor diode-basedcircuit topologies and a high performance varactor diode processtechnology has been presented, which, for a given diode power-lawcapacitance coefficient (m≧0.5), can act as variable capacitors withextremely low distortion. However, the proposed solutions have linearityconstrains for modulated signals or signals with narrow tone spacingwhen considering practical implementations. The invention presented hereaims to overcome these limitations, in terms of linearity for narrowbandsignals, sensitivity to leakage currents of the varactors, high controlvoltage and capacitance tuning range.

SUMMARY OF THE INVENTION

According to the present invention, a varactor element according to thepreamble defined above is provided, in which the varactor element has anexponential depletion capacitance-voltage relation, as defined in theappended claim 1. Such a capacitance voltage relation, in the form ofC_(BBshort)(V)=a₁e^(a) ² ^(V), in which C(V) is the depletioncapacitance as function of the total (reverse) voltage V across thevaractor element, and a₁ and a₂ are predefined constants, allows todesign many applications in which linearity for narrowband signals,sensitivity to the varactor leakage current, high control voltage andcapacitance tuning range are important design constraints.

The exponential depletion capacitance-voltage relation is obtained byproviding a predetermined doping profile in the junction region. Byselecting a predetermined doping profile different from the knownuniform or hyper-abrupt doping profile, the exponentialcapacitance-voltage relation of the varactor element may be obtained.

The junction region comprises, in a further embodiment, a filling layerin an interval of distances lower than x_(low) with a dopingconcentration N_(fill) lower than the doping concentration at distancex_(low)(N(x_(low))). This allows to maintain the N/x² doping versusdepth relation with respect to the junction position. The low dopingconcentration in the filling layer results in a lower contribution tothe electric field in order not to lower the intended breakdown voltageof the diode or unnecessary increase the required control voltages.

The junction region comprises a single sided junction, e.g. a Schottkydiode or a PN junction diode with the one side of the junction dopedsignificantly higher then the intended region for depletion, and thevaractor element is e.g. provided with a doping profile substantiallydefined by N(x)=N/x², N(x) being the varactor element's dopingconcentration in one dimension as a function of x, x being a distancefrom the (effective) junction, and N being a predefined dopingconcentration constant. Especially in electronic circuit design formodulation of RF signals, in which third order inter modulation shouldbe suppressed, such varactor elements can be advantageously applied,even when narrow tone spacing signals are involved.

In a further embodiment, the doping profile is substantially equal toN(x) at least in the interval x_(low) . . . x_(high) in which x_(low) isnearer to the junction than x_(high). This allows to obtain a profilehaving a doping concentration of feasible values (the above formulawould become singular for x=0). The ratio of x_(high) and x_(low)defines the useful capacitance tuning range.

The junction region of the varactor element may also be a two sided ordouble sided junction. To obtain the exponential relation in this caseis more complicated, but certainly attainable in many different manners,e.g. using a more complex doping profile. An example of a double sidedjunction could be for example the use of a low P-type doping for thefilling layer, which in normal varactor operation is completelydepleted. Note that in such a implementation although the dopingjunction is moved, the resulting C(V) relation can still show thedesired exponential dependency on the voltage.

In known circuit arrangements, low distortion varactor operation forlarger tone spacing is accomplished by utilizing two back to backvaractor diodes utilizing a uniform doping, or for hyper abruptvaractors (grading coefficient m>0.5) utilizing a parallel configurationof two anti-series varactor diodes. The known varactors configurationsbehave only linear if the impedance connected to the center tap issignificantly higher than the impedance offered by the varactor diodecapacitances itself, this condition should be satisfied for allfrequency components involved. In practice this proves to be veryproblematic for two tone signals with narrow tone spacing or modulatedsignals. The above can be easily understood by considering a two-tonetest signal with a tone spacing approaching zero. As consequence theimpedance offered at the difference frequency (f₂−f₁) by the varactordiodes will approach infinity when f₁ approaches f₂. It is obvious thatthis yields an unrealistic condition for the center tap impedance whichhas to be larger then the impedance offered by the diodes. Typicallyvery high center tap impedances are required in the conventionalsolution. This give rise to various problems, since the center tap ismore or less “floating”. When using a high valued resistor for thecenter-tap impedance also any leakage current of the varactor diodesbecomes problematic due to resulting DC offsets of the center tap inrespect to the control voltage. Some improvement can be obtained forthis situation by using an anti parallel diode configuration in thecenter tap path in order to increase the AC center-tap impedance.Although good results have been achieved in simulation with thisconfiguration for moderate tone spacing, the use of narrow tone spacingremains problematic and also this configuration is still relativesensitive to leaking currents of the varactor diodes.

The solutions above might provide reasonable performance of theresulting tunable capacitor where static loading conditions arerequired, but are less suited when fast modulation of the tunablecapacitor is needed. Note that these conditions typically apply inmodulators, dynamically varied phase shifters, or adaptive matchingnetworks for dynamic load line modulation mixers, etc. Other shortcomings are the limited capacitance tuning range and high controlvoltage when using a uniform doping profile. When using the hyper abruptvaractors the linearity is somewhat degraded compared to uniformly dopedvaractor implementation.

In a further aspect of the present invention, it is therefore proposedto provide a varactor stack circuit arrangement, comprising two varactorelements according to an embodiment of the present invention, eachhaving two terminals, in which the two varactor elements are connectedin an anti-series configuration, such that a control node is provided bytwo interconnected terminals and two RF connection nodes by the otherterminals. Such an arrangement, also called narrow tone spacing varactorstack (NTSVS), provides an improved performance compared to existingarrangements. The two varactor elements may be connected to each otherusing a common cathode, or using a common anode. This allows thepossibility to choose what kind of control voltage (positive or negativerelative to the RF terminals) can be used in the varactor circuitarrangement. The varactor elements used in this arrangement may beidentical.

In a further embodiment, the varactor circuit arrangement furthercomprises a center tap impedance connected to the control node, thecenter tap impedance providing a low impedance path for base bandfrequency components between the control node and each of the two RFconnection nodes. A high impedance path for fundamental and higher orderharmonic frequency components may also be provided. The indications lowand high impedance refer to the impedance offered by the varactorcircuit arrangement itself for the frequency component underconsideration. This results in a varactor circuit arrangement having ahigh linearity for modulated signals and narrow tone spacings, and ahigh tuning range compared to uniform doped varactors. Only low controlvoltages are needed, and the arrangement is not sensitive for leakagecurrent of the varactor diodes. Furthermore, no high impedance conditionis required at the base band frequencies making it more suitable for theimplementation of modulators, mixers and dynamic/adaptive matchingnetworks.

The low impedance path has an impedance lower than the one offered bythe varactor element capacitances for the base-band frequency component,which allows for a very efficient suppression of third order intermodulation distortion in the varactor circuit arrangement.

The NTSVS may be applied in numerous applications, as part of morecomplex circuitry. In an even further aspect, the present inventionrelates to a four port electronic device, comprising two seriescapacitors and two cross connected capacitors, in which one of the twoseries capacitors is connected between a first input port and a firstoutput port, the other of the two series capacitors is connected betweena second input port and a second output port, one of the two crossconnected capacitors is connected between the first input port and thesecond output port, and the other of the two cross connected capacitorsis connected between the second input port and the first output port. Atleast the two series capacitors or the two cross connected capacitorscomprise a varactor stack arrangement according to an embodiment of thepresent invention. The other capacitors may then be fixed capacitors. Ina very advantageous embodiment, all four capacitors are voltagecontrolled variable capacitors implemented using the varactor stackarrangement according to the present invention. Such a four portelectronic device, or differential varactor amplitude modulator (DVAM),may be applied directly as amplitude modulator, but may also be appliedin more complex circuitry, such as a transmitter, polar amplifiercircuit, and a direct modulator.

In a further embodiment, the four port electronic arrangement furthercomprises a first shunt inductor connected between the first and secondinput port, and a second shunt inductor connected between the first andsecond output port. This allows this circuitry to be used as anamplitude modulator or as an adaptive matching network. Compared toconventional designs, far less components are needed. Also, incombination with an RF amplifier stage, this arrangement may beadvantageously used in a transmitter, allowing a very high power addedefficiency (PAE) for modulated signals or (slowly) varying output powerconditions. Also, polar amplifiers may be designed in which theamplifier efficiency is boosted by saturated operation of the activecomponents in the polar amplifier. At the output of the amplifier,square wave like signal conditions result. Using the four portelectronic arrangement of the present invention in this case, allows toobtain a highly efficient polar amplifier.

In an even further aspect, the present invention relates to a directpolar modulator, comprising a four port electronic arrangement accordingto the present invention, in which the first and second output ports arefurther connected to a series of phase shift sections, each phase shiftsection comprising a varactor stack arrangement according to anembodiment of the present invention. Each of the varactor stackarrangements (in the amplitude modulator and in the phase shiftsections) can be controlled using control voltages. E.g. a digital toanalogue converter may be used to set all control voltages of thevaractor stack arrangements. Such a modulator structure can be part of atransmitter which is directly capable to serve many different modulationformats, such as QPSK, BSK, FSK, OFDM, etc. Also, multiple frequencybands can be accommodated by offsetting the varactor stack arrangementvalues in a proper way.

The present invention also relates to the use of a varactor stackarrangement according to an embodiment of the present invention, inadaptive or dynamic matching networks, in adaptive or tunable phaseshifter devices, in direct modulators arrangements, as up convertingmixer or modulator, in RF switches, in tunable filters or multiplexers,etc. A further example includes the use of a varactor stack arrangementin antenna array systems, such as phased arrays to perform adaptive beamforming.

SHORT DESCRIPTION OF DRAWINGS

The present invention will be discussed in more detail below, using anumber of exemplary embodiments, with reference to the attacheddrawings, in which

FIG. 1 shows a doping profile diagram of an embodiment of the varactorelement according to the present invention having a single sidedjunction;

FIG. 2 a shows a doping concentration versus depth profile of a furtherembodiment of the varactor element according to the present invention(in this doping profile the effective junction is located at 0.2 μm),and FIG. 2 b shows the associated capacitance-voltage characteristic;

FIG. 3 a shows a general symbol for a controlled variable capacitor, andFIGS. 3 b and c show embodiments of such a capacitor using ananti-series arrangement of two variable capacitance varactor diodes;

FIG. 4 shows a schematic circuit diagram of an embodiment of theanti-series arrangement using varactor diodes, as used for varioussimulations;

FIG. 5 shows the resulting spectrum of the capacitive current flowingthrough the varactor stack in the circuit of FIG. 4 using conventionalvaractor diodes, when the node c′ is modulated by 3 MHz signal, whileapplying a 1 MHz two-tone signal on a carrier wave of 1 GHz to the RFterminal(s);

FIG. 6 shows the resulting spectrum under the same conditions as in FIG.5 when using varactor elements according to an embodiment of the presentinvention;

FIG. 7 shows a circuit diagram of a differential varactor amplitudemodulator according to an embodiment of the present invention;

FIG. 8 shows the resulting spectrum of a 2 GHz sinusoidal source signalmodulated by a 1 MHz base band signal, using conventional varactordiodes as variable capacitor in the circuit diagram of FIG. 7;

FIG. 9 shows a similar spectrum when using an embodiment of the varactorelement according to the present invention;

FIG. 10 shows a circuit diagram of an amplifier circuit using anembodiment of the four port electronic device according to an embodimentof the present invention;

FIG. 11 a shows the efficiency plotted versus output power for singletone operation of the amplifier circuit of FIG. 10 using loss-lesscomponents, FIG. 11 b shows the efficiency versus output power whenassuming a Q factor of 100 for the passive components, and FIG. 11 cshows the required DC control voltages for the varactor elements;

FIG. 12 shows a schematic diagram of an embodiment of a transmitterarchitecture using a direct modulator based on varactor elementsaccording to embodiments of the present invention;

FIG. 13 shows a circuit diagram of an embodiment of a direct polarmodulator as used in the transmitter of FIG. 12;

FIG. 14 shows a doping profile diagram of a further embodiment of thevaractor element according to the present invention having a singlesided junction;

FIG. 15 shows a low distortion configuration for varactortuned/modulated narrowband (transmitter) applications of varactorsaccording to an embodiment of the present invention;

FIG. 16 shows a possible configuration of a varactor stack deviceaccording to an embodiment of the present invention comprising twoSchottky diodes;

FIG. 17 shows a top view of terminals of a varactor stack circuitaccording to an embodiment of the present invention;

FIG. 18 a shows a sectional view of a semiconductor structure of avaractor stack assembly according to a further embodiment of the presentinvention; and

FIG. 18 b shows a op view of the varactor stack arrangement of FIG. 18a.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

According to the present invention, a varactor element is providedhaving an exponential capacitance voltage relation, according to

C _(BBshort)(V)=a ₁ e ^(a) ² ^(V)  equation 1

in which C(V) is the capacitance as function of the total (reverse)voltage V across the varactor element, and a₁ and a₂ are constants whichvalue can be chosen based on the application considerations (tuningrange, quality factor of the NTSVS, voltage range).

The capacitance voltage relation of commonly used diode varactors isknown to the skilled person as being equal to

$\begin{matrix}{{C(V)} = \frac{K}{\left( {\varphi + V} \right)^{m}}} & {{equation}\mspace{14mu} 2}\end{matrix}$

in which C(V) is the capacitance as function of the total (reverse)voltage V across the diode, φ is the built-in potential of the diode, mis the power law exponent of the diode capacitance (m=0.5 for a diodewith a uniform doping profile) and K is the capacitance constant.

It has been found that the desired relationship (equation 1) can beachieved by modifying the doping profile of the varactor element,especially the doping profile of the junction region of the varactorelement.

For this purpose a one-side junction (e.g. a Schottky diode) is assumedand solve for the doping profile using the known relation

${N(x)} = {\frac{{C(V)}^{3}}{q\; ɛ}\left( \frac{{C(V)}}{V} \right)^{- 1}}$with $x = \frac{ɛ}{C(V)}$

Making use of the above relations, it can be proven that the requireddoping profile for an exponential capacitance voltage relation in thiscase is:

$\begin{matrix}{{N(x)} = \frac{N}{x^{2}}} & {{equation}\mspace{14mu} 3}\end{matrix}$

in which N is a doping concentration constant to be defined. It shouldbe noted that the upper formulation of the doping profile is singularfor x=0, consequently, measures to avoid this singularity must be taken.In order to explain how the doping profile for a first embodiment of avaractor element according to the present invention should be defined weconsider FIG. 1, which shows the required varactor doping profile for asingle sided junction of the varactor element to achieve the exponentialC(V) relation.

As become clear from FIG. 1 the N/x² doping relation appears as astraight line on logarithmic plot of the doping concentration versus thelogarithm of the distance (x). Since an infinitely high or extremely lowdoping concentration cannot be provided, this relation has to be brokenoff at the distances x_(low) and x_(high). Doing so, automatically theuseful capacitance tuning range (C_(ratio)) is defined since thecapacitance is inversely proportional with the distance x.

C _(ratio) =x _(high) /x _(low)

To achieve the exponential C(V) relation for a single sided junction afilling or “spacer” layer is required in order to satisfy the N/x²doping versus depth relation with respect to the junction position (e.g.a doubling of the distance with the junction should result in a fourtimes lower doping concentration). This spacer or filling layer, whichin the useful varactor diode operation is depleted, preferably does notincrease the electric field significantly to avoid reduced devicebreakdown and capacitance tuning range. To achieve this, the dopingconcentration of this filling layer must be kept low in respect toN(x_(low)). N(x_(low)) must be chosen in such a way that in combinationwith the desired tuning range and control voltage, the zero biasvaractor quality factor is maximized without exceeding the criticalelectric field at the varactor junction for the maximum operationvoltage intended. Since the slope of the doping concentration is fixedby the required exponential capacitance voltage relation, the dopingprofile is basically defined with the choice of: x_(low), x_(high) andN(x_(low)).

As one would expect there is a trade-off in capacitance tuning range,control voltage en Q-factor of the varactor element. For this reason theuse of III-V materials or wide band gap materials is recommended forthis structure. E.g. when using GaAs the intrinsically higher electronmobility (˜a factor 5) of this material compared to silicon, yields a5×Q improvement for an identical structure. However, for low controlvoltages good results can be also obtained using silicon.

Simulations have been performed for a varactor element having a dopingprofile as shown in FIG. 2 a. In this doping profile, the completedoping profile is shown, including the highly doped region (1e+19) leftof the filling layer (5e+16). The lightly doped filling layer in thedoping profile avoids a rapid increase of the electric field near thejunction. This relaxes the device voltage breakdown conditions. Notethat for a one sided junction, this filling layer is provided incombination with the doping concentration of equation 3 to obtain thedesired C(V) characteristic (equation 1), which when plotted on a logscale should results in a substantially straight line as shown in theplot of FIG. 2 b. It must be mentioned that this behaviour ischaracteristic for the proposed doping profile. Any deviation of thestraight line in FIG. 2 b will result in an increase of the IM3distortion level. The related zero bias Q of this particular example islimited to ˜20 for a silicon device. By selecting an other choice forthe parameters of FIG. 1, the voltage range or capacitance tuning ratiocan be adjusted, consequently one can improve for the Q (values>300 arefeasible in silicon), breakdown voltage (values>100V are feasible insilicon for a constrained capacitance tuning range and quality factor)or tuning range (values>15 are feasible in silicon for a constrainedbreakdown voltage and Q factor). Clearly there is a trade off betweenthe Q factor, breakdown voltage and tuning range. One can improve forthis trade of by using other technologies with a higher mobility likeGaAs, which due to its roughly 5× higher mobility compared to silicon,will yield an approximately 5 times higher Q factor for a given varactordoping profile. When considering the device in FIG. 2 the zero bias Qfactor would be approximately 100 when implemented in GaAs. Also the useof wideband gap materials can be beneficial since this allows the use ofhigher doping concentrations and electric field conditions at the devicejunction. The exact doping profile of the filling layer is normally notof great significance to the desired exponential C(V) relation. However,due to the fact that in real devices the abrupt depletion approximationis not very accurate, one can utilize the doping structure of thisspacer layer to improve on the intended exponential C(V) relation forthe low voltage range.

In the above example description, a one sided junction has been used. Ina one sided junction the doping level on one side of the junction ismuch higher than on the other side. As a result the depletion regionwill only effectively extend in one-direction.

However, to obtain the exponential capacitance voltage dependenceaccording equation 1, other solutions to realize this behaviour arepossible if one utilizes two or double-sided junction solutions. In thiscase there are in principle an unlimited number of solutions possiblefor the doping profile which can yield the desired behaviour of equation1.

A varactor element according to any of the embodiments described above,may be advantageously applied as a variable voltage controlledcapacitor. In FIG. 3 a, a general schematic symbol is shown of such avariable voltage controlled capacitor as a three terminal device.Between nodes a and b (or RF connection nodes), a variable capacitanceC_(ab) is present, and node c is used as control voltage input. Actualimplementations using varactor diodes are shown schematically in FIGS. 3b and 3 c, which show two varactor diodes D1, D2 each having twoterminals, connected in anti-series configuration between nodes a and b.Node c is formed by the connecting point of two of the terminals of thediodes (cathode of the diodes in FIG. 3 b, anodes of the diodes in FIG.3 c). FIG. 3 b shows a common cathode implementation, intended for apositive control voltage at node c relative to the nodes a and b andFIG. 3 c shows a common anode implementation, intended for a negativecontrol voltage at node c relative to the terminals a and b. Usingvaractor elements having the desired characteristic of equation 1 asdescribed above, it is possible to build various applications whichbeneficially exploit this characteristic.

In a first exemplary embodiment, the varactor elements are used toprovide a narrow tone spacing varactor stack device. Such an NTSVSdevice may be advantageously used in all sorts of amplitude and phasemodulators, which in turn may be used in adaptive or dynamic matchingnetworks, adaptive or tunable phase shifter devices (e.g. in phasedarray systems), direct modulators, up converting mixers or modulators,RF switches, tunable filters or multiplexers, etc.

The invention introduced here, the “Narrow Tone Spacing Varactor Stack”(NTSVS), is a low distortion tunable capacitor which provides excellentlinearity for narrowband or modulated signals, making it very attractivefor transmitter or modulator applications. The tunable capacitor isbased on two back-to-back varactors with a very specific (N/x²) baseddoping profile (assuming a single sided junction). The configurationutilizes base-band shorts at the center tap and external pins. Such anNTSVS features a high linearity for modulated signals and narrow tonespacings, a high tuning range compared to uniform doped varactors, lowcontrol voltages, is not sensitive for leakage current of the varactordiodes, and no high impedance conditions required at base-band or IFimpedance making it more suitable for the implementation of modulators,mixers and dynamic/adaptive matching networks.

A schematic circuit diagram of a NTSVS is shown in FIG. 4. The NTSVS isused in a common cathode configuration, and the node b of bottom diodeD2 is connected to ground. The node a of the upper diode D1 is connectedto a signal source V_(s) via a resistor R_(g). The signal source V_(s)is grounded at the other side, and provides a two tone signal (indicatedby s₁ and s₂) with a narrowband spacing. A control voltage V_(control)is applied to the control node c′ of the varactor stack, by means of acenter tap impedance Z_(c)(s) of which the other terminal is connectedat node c. The diodes D1 and D2 may be identical.

In known arrangements using a stack of varactor diodes, it is assumedthat Z_(c) can be considered as infinitely high impedance for allfrequency components. When solving for this situation the third orderinter modulation (IM3) component of the voltage on the connectingterminal of the varactor configuration the following expression isfound:

$\begin{matrix}{{{IM}\; 3_{z_{c} = \infty}} = \frac{3\left( {{2s_{1}} - s_{2}} \right)\left( {{2c_{1}^{2}} - {c_{0}c_{2}}} \right)g_{s}^{2}A^{2}}{4{c\left( {{2g_{s}} + {s_{1}c}} \right)}\left( {{2g_{s}} - {s_{2}c}} \right)\left( {{\left( {{2s_{1}} - s_{2}} \right)c} + {2g_{s}}} \right)}} & {{equation}\mspace{14mu} 4}\end{matrix}$

in which:

$\begin{matrix}{c_{0} = \frac{{q(v)}}{v}} \\{c_{1} = {\frac{1}{2}\frac{^{2}{q(v)}}{^{2}v}}} \\{c_{2} = {\frac{1}{6}\frac{^{3}{q(v)}}{^{3}v}}}\end{matrix}$

are the Taylor coefficients of the varactor diode, g_(s) is the sourceconductance (1/R_(g)) and s₁ and s₂ are the complex frequencies, while Ais the amplitude of the voltage signal source. It can be observed fromequation 4 that the IM3 distortion is cancelled when we satisfy thefollowing condition for the varactor Taylor coefficients.

c ₀ c ₂−2c ₁ ²=0

Solving this differential equation for the capacitance function, whileassuming an equal area of the varactor diodes in FIG. 4 yields, the wellknown C(V) textbook relation (equation 2 above), with m=0.5.

${C(V)} = \frac{K}{\left( {\varphi + V} \right)^{m}}$

When solving the IM3 component of the arrangement of FIG. 4 (againassuming an equal area of the varactor diodes) but now using thecondition Z_(a(f2−f1)=)0 (base band short), while Z_(c) is infinitelyhigh for all other frequency components, the following IM3 cancellationcondition is found for very narrow tone spacing (Δf→0):

${{IM}\; 3_{BBshort}} = \frac{\left( {{2c_{1}^{2}} - {3c_{0}c_{2}}} \right)g_{s}^{2}s_{c}A^{2}}{4{c\left( {{2g_{s}} - {s_{c}c}} \right)}\left( {{2g_{s}} + {s_{c}c}} \right)^{2}}$

The resulting C(V) relation, which can be found by solving thedifferential equation,

3c ₀ c ₂−2c ₁ ²=0

proves now to be an exponential relation rather then the well known textbook C(V) relation (equation 2), and is given by:

C _(BBsshort)(V)=a ₁ e ^(a) ² ^(V)

In this relation a₁ and a₂ indicate the integration constants, which addsome flexibility to our solution. Note that any choice of a₁ and a₂ willsatisfy the differential equation, yielding perfect cancellation of theIM3 distortion component also for narrow tone spacing. The varactorelement embodiments as described above fulfil this exponential relationand may advantageously be used in an NTSVS arrangement as shown in FIG.4 to obtain the desired IM3 distortion cancellation.

For this IM3 cancellation, a low AC impedance path at the base-bandfrequencies (this is relative to the AC impedance offered by thevaractor capacitance itself) between the center node c and the RFterminals a and b is needed. Simultaneously, for the high frequencycomponents (fundamental, and higher harmonics) the AC impedance betweenthe node c and node a, or node c and node b must be high (this againrelative to the AC impedance offered by the varactors itself at thesefrequency components).

Using the configuration of FIG. 4 we have simulated the Voltage IP3 ofthe capacitance currents as function of tone spacing, for an existingsolution using a distortion free varactor stack (DFVS) and for asolution using the now proposed NTSVS. In the DFVS, the ratio of crosssectional areas of the two diodes are adapted to minimize third orderdistortion. It has been found that while the conventional DFVS providesthe highest linearity for large tone spacing for a given center tapimpedance, the NTSVS provides the best results for small values of Δf.The cross sectional areas of the two diodes may be the same in the caseof the NTSVS. It is important to note that there must be a low impedance(relative to the impedance offered by the varactor diodes) path for thebase-band frequency component between the center tap and the externalpins. The corner frequency where the linearity starts to degrade isrelated to how well one succeeds to provide low impedance for thebase-band frequencies and simultaneously provide high impedance for thefundamental and higher harmonic frequency components. As a result a moresophisticated network can provide improvements.

All impedance levels indications are relative to the varactor diodeimpedance at the harmonic component under consideration. The NTSVS canbe effectively used for static conditions e.g. to tune out antennamismatch condition, adaptive matching, switching, phase shifting etc.,but can also be used dynamically to implement modulator or mixingfunctions.

In order to create a useful linear mixing function using the arrangementof FIG. 4, two basic conditions should be fulfilled, namely:

-   1) The capacitive current flowing though the effective capacitance    of the varactor stack c_(ab) should be linearly related to the    applied RF voltage over the nodes a and b. In most practical    (telecommunication) applications this requires a zero value for the    3^(rd) order Volterra kernel of c_(ab) with respect to the applied    RF signal over the nodes a and b. Consequently, no third-order    intermodulation distortion products arise in the resulting current    through c_(ab).-   2) For the desired mixing action, the effective capacitance c_(ab)    must be modulated in such a way that the desired transfer function    of the total circuit is modulated in a linear fashion. This has as    consequence that one should compensate (pre-distort) for the    non-linear C(V) relation of c_(ab) with respect to the center tap    voltage at node c, as well for how a capacitance change relates to    transfer function of the total circuit.

Condition 1) is the most important one, since distortion at the RFsignal level can not easily be encountered for. Condition 2) is lesscritical since the controlling voltage in a modulator is typically abase-band signal, which can be accurately controlled or pre-distorted ina rather arbitrary fashion.

In the following examples, a two-tone RF voltage source V_(s) isconnected to node a. The capacitance is modulated by an independentvoltage source (V_(control)) connected to node c. Depending on the C(V)relation, this modulating voltage is pre-distorted using a set ofequations and a non linear pre-distorting element. As a result a linearvariation of c_(ab) with the modulating base-band signal is obtained andconsequently the desired capacitive mixing action. It must be mentionedthat this mixing is perfectly linear under the constraint that c_(ab)does not generate any inter modulation distortion due to the applied RFvoltage at the nodes a and b.

When using the Distortion Free Varactor Stack (DFVS) configuration inthe schematic of FIG. 4 the resulting spectrum of the capacitive currentas shown in FIG. 5 is obtained. The AM side bands around the centerfrequency are visible, but the result is rather bad in terms of the IM3components, which appear around the two-tone signals.

In contrast to the DFVS, the NTSVS requires a base-band short in orderto guarantee its low distortion operation. Consequently, for its correctoperation low impedance paths at base-band frequencies (BB-shorts) haveto be provided between the center tap (node c) and the a and b nodes,and high impedances for the fundamental and higher harmonics. Theresulting spectrum of the capacitive current is given in FIG. 6. For afair comparison the two-tone signal conditions, the effectivecapacitance value c_(ab) and its relative change, are chosen the same asin the DFVS simulation experiment. The spectrum of the capacitivecurrent is significantly improved compared to the results for the DFVSin this mixing experiment. It should be noted that the minimum intermodulation levels achieved in this experiment are now basicallydepending on, how well one can meet the short conditions at thebase-band frequencies and the open conditions at the fundamental andhigher harmonics.

In summary, the NTSVS topology provides, as compared to the previousstate of the art, a high linearity for modulated signals and narrow tonespacings, a high tuning range compared to uniform doped varactors.Furthermore, only low control voltages required for large capacitancevariation, and the arrangement is not sensitive for leakage current ofthe varactor diodes. Also, no high impedance conditions are required atIF impedance making it more suitable for the implementation ofmodulators, mixers and dynamic/adaptive matching networks.

A further advantageous use of the varactor element according to thepresent invention can be found in the following exemplary embodiment.The differential varactor based Amplitude Modulator (DVAM) is based onthe combination of direct and cross wise connected capacitive couplingof the in- and output, as shown in the schematic diagram of FIG. 7. Oneof the two series variable capacitors (Cseries1) is connected between afirst input port and a first output port, the other of the two seriesvariable capacitors (Cseries2) is connected between a second input portand a second output port. One of the two cross connected variablecapacitors (Ccross1) is connected between the first input port and thesecond output port, and the other of the two cross connected variablecapacitors (Ccross2) is connected between the second input port and thefirst output port. Furthermore, the input ports and output ports areconnected to each other using shunt coils (Lshunt). At the input ports,a voltage source Vsource is connected (e.g. providing a 3V 2 GHz signal)and at the output ports, a load (Rload) is connected.

The principle of this configuration is based on the fact that thedisplacements currents through the directly connected capacitors(Cseries1, Cseries2) are in opposite phase with those of the crosscoupled capacitor pair (Ccrossl, Ccross2). When the circuit is drivendifferentially and all the capacitive elements have the same value, thecapacitive currents will cancel. By varying the value of the cross wiseconnected capacitors (Ccross1, Ccross2) in respect to the directconnected capacitors (Cseries1, Cseries2), the displacement currentswill not cancel and energy will be transferred from the differentialinput to output port or visa versa. By combining this capacitive quadwith two shunt inductors (Lshunt) and proper dimensioning of its elementvalues, some very special properties can be achieved for this circuitconfiguration, which makes it attractive as amplitude modulator in RFapplications and in special applications, such as adaptive matchingnetwork in combination with a RF power amplifier stage. Note that such acombination facilitates in principle very high power added efficiency(PAE) for modulated signals or (slowly) varying output power conditions.

Although the above described embodiment uses varactor elements for allfour capacitors, embodiments are also possible in which either the crossconnected capacitors or the series connected capacitors are formed byfixed capacitors (not variable).

The unique behaviour of this circuit can be best studied by enforcingthat the input impedance is ohmic. The input impedance of thisconfiguration is given by:

$z_{in} = \frac{\left( {{s^{2}*{Lc}_{series}} + {s^{2}{Lc}_{cross}} + {2g_{1}{sL}} + 2} \right){sL}}{\begin{pmatrix}{{2s^{4}L^{2}c_{series}c_{cross}} + {s^{3}L^{2}c_{series}g_{1}} + {2s^{2}{Lc}_{series}} +} \\{{s^{3}L^{2}c_{cross}g_{1}} + {2s^{2}{Lc}_{cross}} + {2g_{1}{sL}} + 2}\end{pmatrix}}$

Enforcing the imaginary part of Z_(in) to be zero yields the followingrelation for the series and cross connected capacitors

${c_{cross} = \frac{- \left( {{\omega^{2}{Lc}_{series}} - 2} \right)}{\left( {\omega^{2}L} \right)}},{c_{cross} = \frac{- \left( {{{- \omega^{2}}{Lc}_{series}} + 1 + {g_{load}^{2}\omega^{2}L^{2}}} \right)}{\left( {\omega^{2}{L\left( {{\omega^{2}{Lc}_{series}} - 1} \right)}} \right)}}$

in which:

c_(series)=series capacitor value

c_(cross)=cross connected capacitor value

g_(load)=single ended load conductance

L=shunt connected inductor

By now changing the value of the C_(series) versus c_(cross) whilesatisfying the above condition for the values of C_(series) andC_(cross), the following properties are achieved.

The transfer (s₂₁) can be continuously varied between −j and +j;

The input impedance is always ohmic.

As a result, this circuit will not introduce any AM to PM (phasemodulation) distortion, since the phase of s₂₁ is always on theimaginary axis. The phase reversal indicates the potential operation asmultiplier. The fact that the circuit is lossless results in areflection of all energy (s₁₁=s₂₂=1) when no power is transferred(s₂₁=s₁₂=0) from in- to output (C_(series)=C_(cross)), yielding aninfinitely high impedance at the ports. (Note that an inverse behaviour(s₁₁=s₂₂=−1) is also possible if one uses series inductors rather thenshunt inductors yielding short circuit conditions at the ports). Thefact that the input impedance varies with the power transfer makes thenetwork interesting for dynamic load line applications. Furthermore, theoperation frequency of this network can easily customized by adjustingthe values of the variable capacitances c_(cross), and c_(series).

Above, the small signal behaviour of the DVAM has been studied. Itsprinciple is based on the use of tunable capacitances for theimplementation of the series and cross connected capacitors. It istherefore logic to consider varactors for this purpose. In the followingsimulation experiment we will compare the large signal performance ofthe DFVS and the NTSVS for this amplitude modulator. It will be shown,that the proposed varactor structure of the present invention, usingbase band shorts will provide superior performance over the DFVS in thisapplication.

When using ideal variable capacitors, applying a 2 GHz sinusoidalvoltage with 3 V signal amplitude at the input of the DVAM, andmodulating the values of c_(series) and c_(cross) using a low frequency(base band) sinusoidal signal of 1 MHz, would result in a perfectlymultiplied signal, i.e. a two tone signal with an ideal spectrum (1.999GHz and 2.001 GHz) without any inter modulation effects (especiallythird order IM).

When using the earlier described distortion free varactor stacks (DFVS)as variable capacitors, the spectrum shown in FIG. 8 is obtained. Interms of third order inter modulation (IM3) this spectrum is very bad.

When using NTSVS devices according to one of the embodiments of thepresent invention (with an N/x² doping profile), again, a low impedancepath for the base-band frequencies between the center tap node and RFterminals of the NTSVS devices is provided. If a high valued inductor isused to connect the modulating voltage to the center tap of each NTSVS,these conditions are automatically fulfilled. This is a big advantage incontrolling the capacitance to its desired value. The spectrum of thetwo-tone signal generated using this circuit topology for the samesignal conditions as before is given in FIG. 9. As can be noted fromthis experiment now a very clean two-tone signal is obtained of morethan 70 dBc using a 3V amplitude swing at is input. This is an importantresult since it indicates that using a varactor device with a specialbut realistic doping profile a close to ideal non dissipative amplitudemodulator can be implemented.

In a further embodiment of the present invention, NTSVS varactorelements are used in a polar amplifier circuit, of which the schematicdiagram is shown in FIG. 10. Currently, people are considering polaramplifiers concepts to improve on spectral noise, efficiency andflexibility in terms of serving multiple communication standards. One ofthe common characteristics of these amplifiers is the saturatedoperation of the active device(s) in order to boost the amplifierefficiency. This saturated operation results in square wave like signalconditions at the output of the amplifier. However, due to the saturatedoperation of the amplifier, the output power is no longer linearlyrelated to the input power. To solve for this problem currently in polaramplifier implementations, dynamic supply voltage modulation isconsidered to control the amount of output power. Although, having someadvantages there are the following complications with this approach:

A highly efficient DC to DC converter is required;

Switching noise of the DC-to-DC converter requires extensive filteringresulting in the use of unrealistically large circuit implementations;

Voltage modulation results in AM-PM modulation by the active devices,consequently pre-distortion is required.

An alternative for the dynamic voltage modulated polar amplifier conceptis to make use of dynamic loading of the output stage in order tocontrol the amount of output power. Using the DVAM topology as describedin the embodiments above, it is quite easy to implement this. Althoughthis can be done in various ways, an exemplary embodiment is shown inFIG. 10. In this FIG. 10 the DVAM (comprising varactor elements D1 . . .D8, shunt inductors Ls1 . . . Ls4, in which the control points of eachNTSVS stack are indicated by Vcsd1, Vccd1, Vccd2, and Vcsd2,respectively) performs the dynamic matching and modulation function. TheDVAM is controlled by base-band signals which ensure the desiredcapacitance modulation of the NTSVS devices. All components levels andcontrol signals can be chosen in respect to the desired output power,supply voltage and capacitance tuning range. Additional stubs Z1 and Z2at the output of transistors T1 and T2 are for the biasing and toprovide short conditions for the even harmonics. Additional seriesresonators are provided using inductances L1, L2 and capacitors C1, C2,respectively. The additional series resonators (center frequency fo) areadded to provide a high impedance for the odd harmonics, both arerequired in order to obtain the highest power added efficiency (PAE).The PAE versus output power when ideal transistors (Default Gummel Poonmodel) with lossless inductors and varactors are assumed are given inFIG. 11. The power sweep is obtained by changing the static voltages ofthe varactor in DVAM structure. The graph of FIG. 11 a shows theefficiency plotted versus output power for single tone operation of theamplifier using loss-less components. The graph of FIG. 11 b providesthe results when assuming a Q of 100 for the passive components. In thegraph of FIG. 11 c the required DC control voltages for the NTSVSelements are plotted against the power (upper trace for the crossconnected varactor elements and the lower trace for the series connectedvaractor elements). It can be observed that a very high efficiency canbe obtained over a large power control range. Also the required controlvoltages are limited in value Further optimization of the circuit interms of component values and or impedance levels can reduce therequired control voltages even more.

In a further embodiment of the present invention, a direct modulator isproposed which combines a DVAM with a variable phase shifter, as shownin the schematic diagram of FIGS. 12 and 13. In this embodiment, theamplitude and phase shift can be set by the control voltages of theNTSVS elements, yielding a polar modulator. Note that such aconfiguration, can considerably simplify the traditional architecture ofa transmitter while still capable of generating the desired complexmodulated signals, which are typically in use in wireless communication.

The newly proposed transmitter architecture, using a direct modulatorbased on NTSVS elements, is given in FIG. 12. A voltage controlledoscillator (VCO, e.g. based on a phased locked loop PLL) 21 provides acarrier wave to a power amplifier (PA) 22. The output of the PA 22 isprovided to a direct modulator 23, of which an implementation is shownin FIG. 13 described below. The direct modulator 23 receives controlvoltages for the NTSVS elements from a digital to analogue converter 24(D/A), which in its turn is supplied with digital input data formodulating the carrier wave. The output of the direct modulator 23 thenprovides the modulated signal.

As can be noted from this figure, the NTSVS elements in the modulatorare controlled for their capacitance value by the voltages delivered bythe digital to analogue converter 24, which operates at, or at amultiple of the base-band frequency. This concept eliminates the needfor many RF function blocks in conventional transmitter designs. Bycontrolling the transfer of the polar modulator in a time variant way,the constellation diagram of the desired modulation can be obtained. Byalso accurately controlling the transitions between the constellationpoints in the proper fashion, the resulting frequency spectrum at theoutput of the polar modulator can be adjusted to meet the communicationstandard requirements under consideration. Note that this basicallyeliminates the need of intermediate filters in conventional amplifierimplementations. Consequently, the resulting transmitter structure isdirectly capable to serve many different modulation formats, dependingon the desired communication standard (e.g. QPSK, BSK, FSK, OFDM etc) byjust changing the input of the digital input of the D/A converter 24.Note that now complex modulation schemes can be generated without theneed of linear RF circuit blocks for the mixers and power amplifier.This will result in a power reduction of the total transmitter.

Since the NTSVS elements are tunable, also multiple frequency bands canbe easily addressed by offsetting the NTSVS values in the network in aproper way (e.g. as discussed above in relation to the DVAMembodiments). The phase shifter, when based on all pass networks or onan artificial transmission line concept, composed out off many LCsections in which the capacitive elements are implemented by NTSVSelements, is wide band in nature itself, yielding a frequencyreconfigurable network. Note that such a network can have considerableadvantages when aiming for multi-communication standards ormulti-frequency band transceivers since no intermediate filters or other(reconfigurable) RF functions are required. The proposed setup can alsobe useful for low power very high frequency transmitter implementations,since less power for the otherwise power hungry RF circuit blocks arerequired.

A potential implementation example of such a direct modulator is shownschematically in FIG. 13. In this schematic the DVAM (see embodiment ofFIG. 7) is followed by an artificial transmission line composed out offn LC sections, each comprising four transmission inductances (Ltrans1 .. . . Ltrans4) and a capacitance element Cshunt. The capacitive elementsCshunt are implemented by NTSVS elements. By changing the controlvoltages of the NTSVS elements, any phase shift or amplitude can beachieved. In this configuration benefit is obtained once again from theproperties of the DVAM network that the input impedance tracks with thedesired output power, facilitating again the implementation of a highlyefficient amplifier but now using a direct modulator with base-bandcontrol. It must be mentioned that many network topologies are possiblefor the amplitude and the phase modulator that result in similarproperties as shown here. Also single-ended versions are possible.Essential in all these solutions is a tunable capacitive element thatallows fast tuning and that does not cause any inter modulationdistortion, the NTSVS device according to embodiments of the presentinvention being such a component.

Using a DVAM implementation with NTSVS devices according to the presentinvention, a number of advantages may be achieved:

Provides low Q impedance transformation (matching) between in andoutput;

Signal transfer (s₂₁) can be controlled between −1 through 0 to 1;

Structure can be easily customized for the available tuning range of thevaractor;

Low control voltages required;

The 180 phase reversal in S₁₂ makes it a perfect up-converting mixer;

No phase variation during tuning (no AM-PM distortion);

Yields ohmic loading conditions at in- and output over whole tuningrange;

Tuning range can be selected between a fixed impedance and infinity;

Tuning range can be selected between a fixed impedance and short circuitconditions at fundamental;

Operating frequency can be easily tuned by changing the bias conditionsof the varactors;

Perfectly linear in combination with NTSVS diode for both sinusoidal aswell square wave input signals.

Although the examples given in this document are mostly differential innature, also single ended versions are very well possible to realize thedesired circuit functions (namely, static or dynamic loading/outputpower control as well phase shifting trough the used of NTSVS basedelements). This can serve many actual applications in telecommunicationand radar systems.

In FIG. 14, a more detailed view is shown of a Q optimized varactordoping profile for varactor tuned or modulated linear narrowbandapplications. In these embodiments, the following profile constraintsare applied:

-   -   The useful capacitance tuning ratio which is defined by ratio        X_(high)/X_(low), ranges for practical and useful        implementations from 2 to 15, or even higher ratios.    -   Region 1) Spacer layer.        -   0 Spacer layer thickness    -   The spacer layer is required to ensure the proper doping        relation versus distance in region 2. The thickness of the        spacer layer is in principle equal to X_(low):        -   X_(low) can range from 0.03 μm for low voltage applications            (V_(breakdown)<5V) to 0.3 μm for high voltage applications            (V_(breakdown)>40V) (see also table 1). Significantly lower            or higher voltage ranges might widen the above constraints    -   In practical implementation the exact location of the junction        is important in order to avoid linearity degradation when the        varactor is applied in the appropriate circuit configuration.        The exact location of the junction needs to be at x=0 within a        tolerance of +/−0.2*X_(low).        -   0 Spacer layer doping/sheet resistance    -   The exact doping of the spacer layer has not too much effect on        the intended linearity rather than a shift in control voltage.        However the doping of the spacer layer will give rise to an        undesired increase in the electric field causing restrictions on        the achievable compromise in device breakdown-tuning        range-quality factor. For this reason the doping concentration        in the spacer layer needs to be restricted. If we assume set        that the increase in electrical field due to the doping of the        spacer layer should not exceed half the value of the critical        electrical field e.g. in silicon

${{\Delta \; E} = {{\frac{1}{2}E_{crit}} = {3 \times 10^{5}\mspace{14mu} {V/{cm}}}}},$

the related sheet resistance of this layer should be higher then2385Ω/□. For materials with other values for the critical field strengthsimilar considerations can be made.

-   -   Region 2) Graded doping profile.        -   This region is responsible for the intended approximated            exponential C(V) relation, which in combination with the            appropriate circuit configuration yields the highly linear            operation. For highly linear operation the grading            coefficient m should be between 1.7 and 2.3. The highest            linearity in for practical implementations is achieved with            m=2.1 rather then 2. This is caused by a cancelling effect            that occurs between third and fifth order distortion            components. It is very important that the C(V) function does            not exhibit any humps and is purely monotonic.        -   The doping concentration N(X_(low)) follows from the            equations 3.7 to 3.11 as given in the detailed description            below, and offers the best quality factor for a given            breakdown and capacitance tuning range. The value of the            effective (activated) doping is typically between 4e18 for            devices with a breakdown voltage of <5V and 1e17 for devices            with a breakdown voltage of >40V (see table I)    -   Region 3) Buried Layer        -   The buried layer should directly connect to the graded            doping profile without introducing significant series            resistance. Varactor implementations from the prior art            suffer from the low doped connection (series resistance)            between the graded profile and the buried layer, lowering            the quality factor of the varactor. The capacitance voltage            relation in these implementations when the depletion region            extends to this region is not relevant for our application            since the intended approximated exponential C(V) relation is            violated, yielding a higher distortion. The series            resistance offered by the buried layer should be            significantly lower than the intrinsic sheet resistance            offered by the region 2. Consequently, for high Q varactor            implementation we require that the sheet resistance of the            buried layer is lower than the intrinsic sheet resistance of            region 2 (e.g. see table I in the detailed description            below).

In FIG. 15, an exemplary embodiment is shown of a low distortionconfiguration for varactor tuned/modulated narrowband (transmitter)applications of varactors according to the present invention (with adoping profile as given in FIG. 15) utilizing baseband “shorts” andharmonic “open” conditions for the fundamental and 2^(nd) harmonicbetween the nodes a and c, and between nodes b and c.

In order to create a low distortion varactor for narrowband modulatedsignals, the varactor configuration of FIG. 15 should be utilized. Theintended tuneable component is connected with its RF terminals a and bto the appropriate place in a tuneable network e.g. adaptive matchingnetwork or filter. In difference to the know low distortion varactorconfigurations, this varactor configuration utilizes baseband “shorts”and “open” conditions for the fundamental and 2^(nd) harmonics betweennode a and c and node b and c and only works well when using varactorswith a doping profile as given in FIG. 14.

In view of FIG. 15 the conditions on the terminal impedance for lowdistortion operation of narrowband modulated signals (<200 MHz bandwidth) are:

|Z _(Basband)|×10<|Z _(diode) |@f _(baseband)

|Z _(fundamental)|>10×|Z _(diode) |@f _(fundamental)

|Z _(second)|>10×|Z _(diode) |@f _(2nd harmonic)

in which Z_(diode) is the impedance offered by the varactor diode inreverse bias at the indicated frequency.

These conditions apply for both diodes and should be satisfiedsimultaneously the individual impedance values offered to D1 and D2 maydiffer, however they should satisfy the upper requirements. The controlvoltage V_(controlD1) and V_(controlD2) can also differ in value butshould keep the diodes in reverse bias.

In FIG. 16, a simple implementation of a varactor stack is given. TwoSchottky diodes (or varactor elements) are formed on top of a buriedlayer 2, in which each Schottky diode comprises a metal layer 4 a, 4 bon top of a doped semiconductor layer 3 a, 3 b. The doping profile ofeach doped layer 3 a, 3 b is according to the embodiments describedabove (see e.g. FIG. 1, 2 a or 14), in which x=0 at the Schottkyinterface (between metal layer 4 a, 4 b and doped layer 3 a, 3 b). Aburied layer 2, connecting the two Schottky diodes by a low impedancematerial, is provided having a low sheet resistance to achieve a highquality factor for large varactor capacitance values. The distancebetween the two Schottky diodes (indicated by ds in FIG. 16) should bekept to a minimum, to be able to keep the impedance between the twoSchottky diodes as low as possible. It is noted that for correctoperation, the correct harmonic terminations should be provided atterminals a, b and c indicated in FIG. 16, as described above.

In an integrated process technology to optimize the Quality factor (Q)of a varactor diode with a large capacitance value, typically a fingerstructure is applied to reduce the influence of the sheet resistance ofthe buried layer 2. In FIG. 17 a top view of the terminal structure ofsuch an embodiment is shown. It will be apparent to the skilled personthat the areas indicated by a, b, and c (corresponding to the terminalsa, b, and c of the embodiment shown in FIG. 3 a, b and c) correspond tothe Schottky diode and control node layers as shown in e.g. FIG. 16.This approach is favoured since the sheet resistance of the buried layer2 in a integrated process technology can not easily reduced to anyextent without rising problems of isolating devices from each other.When implementing a varactor stack for RF applications using the fingerapproach this method works reasonable well for capacitors with a not toohigh capacitance value (e.g. below 5 pF). Since the conditions for thecenter tap impedance (terminal c) are less strict than for the RF paththe connection scheme for this terminal is more relaxed and can belimited to one or two contacts of the total structure.

When considering discrete implementations of the varactor stack with ahighly doped substrate the effective resistance of the buried layer 2and doped substrate between the diodes can be reduced to such an extendthat the finger structure can be omitted. The resulting device is nolonger isolated, but this is no longer a concern since after cutting thewafer the component can be flip chipped on a hybrid circuitimplantation. Note that the harmonic termination of the center tapconnection (terminal c, e.g. an inductor) can be placed on the discretevaractor stack component or the hybrid board.

A drastically way to reduce the effective sheet resistance of the buriedlayer in an integrated process technology which requires isolationbetween individual components is the use of a backside metal contact incombination with micromachining. The intended structure is shown in FIG.18 a. The varactor stack device is indicated by reference numeral 10,and is formed on a silicon or III-V material wafer 11. As in earlierembodiments, the varactor stack device 10 is formed by providing aburied layer 2 having a low sheet resistance, on which two Schottkydiodes are formed by doped layers 3 a, 3 b and metal layers 4 a, 4 b,respectively. Between the Schottky diodes and surrounding the metallayers 4 a, 4 b, a layer of oxide 12 is provided. Note that in thisfigure the backside of the wafer 11 is etched away until the buriedlayer 2 is reached. This etching can be controlled using an etch stoplayer e.g. buried oxide in the case of using a silicon on isolator waferor by similar techniques in III-V materials. By making contact holes inthe etch stopping layer and directly contacting the buried layer 2 orthe lightly doped N region with a thick metal (back metal layer 15), theeffective resistances between the diodes in the RF path can be seriouslyreduced (the two varactor elements being connected by a low impedance(combination of) material(s). Consequently, the sheet resistance of theburied layer 2 is less an issue since the back metal layer 15 takes carefor the conduction of the RF signal. The control terminal 5 (controlnode c of the equivalent diagram of FIG. 3 a-c) can be connected to thefrontside of the wafer through a via. As a result no finger structuresare anymore required on the front side resulting in an effectivereduction of the required wafer area and an improved Q factor. Note thatin this approach there are no high quality vias to the front side of thewafer required The only connection to the front side of the wafer is forthe implementation of the center tap terminal 5 but since this terminalshould only provide a connection for the DC and baseband signals theimpedance requirements are quite relaxed for this connection. In FIG. 18b a top view of the varactor device 10 of FIG. 18 a is shown, indicatingthe positions of the metal contacts 4 a, 4 b, 5. Note that fingerstructures (such as in the embodiment of FIG. 17) at the top side are nolonger needed due to the reduced resistance of the backside metalconnection 15. The structure can be further improved and customized bytaking measures to improve the mechanical stability, e.g. by gluing orgrowing mechanical support layers.

The present invention, its implementations and theoretical backgroundmay be understood in more detail from the following.

1-20. (canceled)
 21. A varactor element having a junction region, inwhich the depletion capacitance of the varactor element varies when areverse bias voltage is applied to the varactor element, wherein thevaractor element has an exponential depletion capacitance-voltagerelation, in which the junction region comprises a single sidedjunction; the varactor element is provided with a doping profilesubstantially defined by N(x)=N/x^(m), wherein N(x) is the varactorelement's doping concentration in one dimension as a function of x, x isa distance from the junction, N is a predefined doping concentrationconstant, and m is an exponential factor; and the junction regioncomprises a filling layer in an interval of distances lower than x_(low)with a doping concentration N_(fill) lower than the doping concentrationat distance x_(low) (N(x_(low))).
 22. The varactor element according toclaim 21, wherein the exponential factor has a value in the range1.7≦m≦2.3.
 23. The varactor element according to claim 21, wherein thedoping profile is substantially equal to N(x) at least in the intervalx_(low) . . . x_(high) in which x_(low) is nearer to the junction thanx_(high).
 24. The varactor element according to claim 21, wherein thejunction region is a two sided or double sided junction.
 25. Thevaractor stack circuit arrangement, comprising two varactor elementsaccording to claim 21, each having two terminals, wherein the twovaractor elements are connected in an anti-series configuration, suchthat a control node is provided by two interconnected terminals and twoRF connection nodes by the other terminals.
 26. The varactor stackcircuit arrangement according to claim 25, wherein the two varactorelements are connected by a low impedance material.
 27. The varactorstack circuit arrangement according to claim 26, wherein the lowimpedance material comprises a back side metallization.
 28. The varactorstack circuit arrangement according to claim 26, wherein the varactorcircuit arrangement further comprises a center tap impedance connectedto the control node, the center tap impedance providing a low impedancepath for base band frequency components between the control node andeach of the two RF connection nodes.
 29. The varactor stack circuitarrangement according to claim 28, wherein the low impedance path has animpedance lower than the varactor element capacitances for the base-bandfrequency components.
 30. The varactor stack circuit arrangementaccording to claim 28, wherein which the base band frequency is theseparation frequency of a signal having a narrow tone spacing or themodulation frequency of a modulated (RF) signal.
 31. A four portelectronic arrangement, comprising two series capacitors and two crossconnected capacitors, wherein one of the two series capacitors isconnected between a first input port and a first output port, the otherof the two series capacitors is connected between a second input portand a second output port, one of the two cross connected capacitors isconnected between the first input port and the second output port, andthe other of the two cross connected capacitors is connected between thesecond input port and the first output port, further wherein at leastthe two series capacitors or the two cross connected capacitors comprisethe varactor stack circuit arrangement according to claim
 26. 32. Thefour port electronic arrangement according to claim 31, furthercomprising a first shunt inductor connected between the first and secondinput port, and a second shunt inductor connected between the first andsecond output port.
 33. A direct polar modulator, comprising the fourport electronic arrangement according to claim 31, wherein the first andsecond output ports are further connected to a series of phase shiftsections, each phase shift section comprising the varactor stackarrangement according to claim
 26. 34. An adaptive or dynamic matchingnetwork comprising the varactor stack arrangement according to claim 26.35. An adaptive or tunable phase shifter device comprising the varactorstack arrangement according to claim
 26. 36. A direct modulatorarrangement comprising the varactor stack arrangement according to claim26.
 37. An up converting mixer or modulator comprising the varactorstack arrangement according to claim
 26. 38. An RF switch comprising thevaractor stack arrangement according to claim
 26. 39. A tunable filteror multiplexer comprising the varactor stack arrangement according toclaim
 26. 40. An antenna array system comprising the varactor stackarrangement according to claim 26.